%------------------------------------------------------------------------------
% File : Beagle---0.9.52
% Problem : GRP010-4 : TPTP v9.0.0. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Apr 9 06:24:44 PM UTC 2025
% Result : Unsatisfiable 2.73s 1.71s
% Output : CNFRefutation 2.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 17 ( 17 unt; 0 typ; 0 def)
% Number of atoms : 17 ( 16 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 17 ( 17 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
%$ multiply > #nlpp > inverse > identity > c > b
%Foreground sorts:
%Background operators:
%Foreground operators:
tff(inverse,type,
inverse: $i > $i ).
tff(multiply,type,
multiply: ( $i * $i ) > $i ).
tff(b,type,
b: $i ).
tff(identity,type,
identity: $i ).
tff(c,type,
c: $i ).
tff(f_34,axiom,
multiply(b,c) != identity,
file(unknown,unknown) ).
tff(f_29,axiom,
! [X] : ( multiply(identity,X) = X ),
file(unknown,unknown) ).
tff(f_32,axiom,
multiply(c,b) = identity,
file(unknown,unknown) ).
tff(f_26,axiom,
! [X,Y,Z] : ( multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)) ),
file(unknown,unknown) ).
tff(f_31,axiom,
! [X] : ( multiply(inverse(X),X) = identity ),
file(unknown,unknown) ).
tff(c_10,plain,
multiply(b,c) != identity,
inference(cnfTransformation,[status(thm)],[f_34]) ).
tff(c_4,plain,
! [X_4] : ( multiply(identity,X_4) = X_4 ),
inference(cnfTransformation,[status(thm)],[f_29]) ).
tff(c_8,plain,
multiply(c,b) = identity,
inference(cnfTransformation,[status(thm)],[f_32]) ).
tff(c_31,plain,
! [X_8,Y_9,Z_10] : ( multiply(multiply(X_8,Y_9),Z_10) = multiply(X_8,multiply(Y_9,Z_10)) ),
inference(cnfTransformation,[status(thm)],[f_26]) ).
tff(c_52,plain,
! [Z_10] : ( multiply(c,multiply(b,Z_10)) = multiply(identity,Z_10) ),
inference(superposition,[status(thm),theory(equality)],[c_8,c_31]) ).
tff(c_59,plain,
! [Z_10] : ( multiply(c,multiply(b,Z_10)) = Z_10 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_52]) ).
tff(c_6,plain,
! [X_5] : ( multiply(inverse(X_5),X_5) = identity ),
inference(cnfTransformation,[status(thm)],[f_31]) ).
tff(c_46,plain,
! [X_5,Z_10] : ( multiply(inverse(X_5),multiply(X_5,Z_10)) = multiply(identity,Z_10) ),
inference(superposition,[status(thm),theory(equality)],[c_6,c_31]) ).
tff(c_73,plain,
! [X_12,Z_13] : ( multiply(inverse(X_12),multiply(X_12,Z_13)) = Z_13 ),
inference(demodulation,[status(thm),theory(equality)],[c_4,c_46]) ).
tff(c_246,plain,
! [Z_17] : ( multiply(inverse(c),Z_17) = multiply(b,Z_17) ),
inference(superposition,[status(thm),theory(equality)],[c_59,c_73]) ).
tff(c_266,plain,
multiply(b,c) = identity,
inference(superposition,[status(thm),theory(equality)],[c_246,c_6]) ).
tff(c_284,plain,
$false,
inference(negUnitSimplification,[status(thm)],[c_10,c_266]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GRP010-4 : TPTP v9.0.0. Released v1.0.0.
% 0.06/0.13 % Command : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 7 21:09:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 2.73/1.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.73/1.72
% 2.73/1.72 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------